Finite Group Databasebeta

← #649085

Subgroups — #649085

Order 512.

3206 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2565C211yesmaximal, characteristic, complemented
2C2×#2442C211yesmaximal, characteristic
3C2×#2360C211yesmaximal, characteristic
4C22×#384C211yesmaximal, characteristic
5#15629C214yesmaximal, complemented
6#15434C214yesmaximal, complemented
7#15240C211yesmaximal, characteristic, complemented
8#15228C211yesmaximal, characteristic, complemented
9#15184C211yesmaximal, characteristic, complemented
10#15151C211yesmaximal, characteristic, complemented
11#14786C214yesmaximal
12#14702C211yesmaximal, characteristic
13#14139C211yesmaximal, characteristic
14#14049C211yesmaximal, characteristic, complemented
15#13976C211yesmaximal, characteristic, complemented
16#13909C211yesmaximal, characteristic, complemented
17#13882C214yesmaximal
18#13881C211yesmaximal, characteristic
19C4×#385C211yesmaximal, characteristic
20C22×#125C2211yescharacteristic
21C22×C22⋊Q8C2211yescharacteristic
22C22×C4×Q8C2211yescharacteristic
23C23×C4⋊C4C2211yescharacteristic
24C23×C4⋊C4C2214yes—
25C23×C4⋊C4C2211yescharacteristic
26C23×C42C2211yescharacteristic
27#2565—28no—
28#2442—28no—
29C2×#400C2212yes—
30C2×#398C2212yes—
31C2×#398C2214yes—
32C2×#398C2214yes—
33#2360—28no—
34C2×#391C2211yescharacteristic
35C2×#391C2211yescharacteristic
36C2×#391C2211yescharacteristic
37C2×#391C2211yescharacteristic
38C2×#391C2211yescharacteristic
39C2×#389C2212yes—
40C2×#389C2211yescharacteristic
41C2×#389C2211yescharacteristic
42C2×#389C2211yescharacteristic
43C2×#387C2214yes—
44C2×#387C2212yes—
45C2×#387C2214yes—
46C2×#385C2212yes—
47C2×#385C2212yes—
48C2×#385C2212yes—
49C2×#384—28no—
50C2×#384C2214yes—
51C2×#384C2211yescharacteristic
52C2×#384C2211yescharacteristic
53C2×#384C2211yescharacteristic
54C2×#384C2211yescharacteristic
55C2×#382C2211yescharacteristic
56C2×#382C2211yescharacteristic
57C2×#382C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2212yes—
60C2×C4×C4⋊C4C2211yescharacteristic
61C2×C4×C4⋊C4C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C22⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2212yes—
65C2×C4×C22⋊C4C2211yescharacteristic
66#1445C2214yes—
67#1445C2214yes—
68#1445C2214yes—
69#1445C2214yes—
70#1444C2214yes—
71#1444C2214yes—
72#1442C2214yes—
73#1441C2214yes—
74#1441C2214yes—
75#1441C2214yes—
76#1441C2214yes—
77#1441C2214yes—
78#1436C2212yes—
79#1436C2214yes—
80#1436C2214yes—
81#1436C2214yes—
82#1436C2212yes—
83C4⋊#95C2211yescharacteristic
84C4⋊#95C2211yescharacteristic
85C4⋊#95C2211yescharacteristic
86C4⋊#95C2211yescharacteristic
87C4⋊#95C2211yescharacteristic
88C4⋊#95C2211yescharacteristic
89C22⋊#95C2214yes—
90C22⋊#95C2212yes—
91C22⋊#95C2214yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8C2311yescharacteristic
96C24×C4C2312yes—
97C24×C4C2312yes—
98C24×C4C2312yes—
99C24×C4C2311yescharacteristic
100C2×#125—24no—
101C2×#125—24no—
102C2×#125—42no—
103C2×C22⋊Q8—24no—
104C2×C22⋊Q8—24no—
105C2×C22⋊Q8Q818yes—
106C2×C4×Q8—24no—
107C2×C4×Q8—24no—
108C2×C4×Q8—42no—
109C22×C4⋊C4—24no—
110C22×C4⋊C4—24no—
111C22×C4⋊C4—216no—
112C22×C4⋊C4—24no—
113C22×C4⋊C4—24no—
114C22×C4⋊C4—216no—
115C22×C4⋊C4—42no—
116C22×C4⋊C4—42no—
117C22×C4⋊C4—48no—
118C22×C4⋊C4C2312yes—
119C22×C4⋊C4C2314yes—
120C22×C4⋊C4C2311yescharacteristic
121C22×C4⋊C4C2311yescharacteristic
122C22×C4⋊C4C2311yescharacteristic
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2312yes—
127C22×C4⋊C4C2312yes—
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2314yes—
130C22×C4⋊C4C2314yes—
131C22×C4⋊C4C2312yes—
132C22×C4⋊C4C2314yes—
133C22×C4⋊C4C2311yescharacteristic
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2312yes—
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2312yes—
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2311yescharacteristic
143C22×C22⋊C4C2311yescharacteristic
144C22×C22⋊C4C2312yes—
145C22×C42—24no—
146C22×C42—24no—
147C22×C42—24no—
148C22×C42C2312yes—
149C22×C42C2311yescharacteristic
150C22×C42C2311yescharacteristic
151C22×C42C2312yes—
152C22×C42C2311yescharacteristic
153C22×C42C2311yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2312yes—
157#400—28no—
158#398—216no—
159#398—28no—
160#398—48no—
161#391—24no—
162#391—24no—
163#391—24no—
164#391—24no—
165#391—42no—
166#389—24no—
167#389—24no—
168#389—24no—
169#389—28no—
170#387—216no—
171#387—28no—
172#387—48no—
173#385—28no—
174#385—28no—
175#385—28no—
176#384—24no—
177#384—24no—
178#384—216no—
179#384—24no—
180#384D418yes—
181#382—24no—
182#382—24no—
183#382—42no—
184#380—24no—
185#380—28no—
186C4×C4⋊C4—24no—
187C4×C4⋊C4—24no—
188C4×C4⋊C4—24no—
189C4×C22⋊C4—24no—
190C4×C22⋊C4—28no—
191C4×C22⋊C4D418yes—
192C2×#95C2312yes—
193C2×#95C2314yes—
194C2×#95C2314yes—
195C2×#95C2314yes—
196C2×#95C2314yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2314yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2311yescharacteristic
221C2×#95C2311yescharacteristic
222C25C2411yescharacteristic
223C22×Q8—22no—
224C22×Q8—22no—
225C22×Q8—22no—
226C22×Q8—22no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8C2×Q814yes—
230C23×C4—24no—
231C23×C4—24no—
232C23×C4—24no—
233C23×C4—22no—
234C23×C4—24no—
235C23×C4—22no—
236C23×C4—24no—
237C23×C4—22no—
238C23×C4—24no—
239C23×C4—22no—
240C23×C4—24no—
241C23×C4—24no—
242C23×C4—28no—
243C23×C4—28no—
244C23×C4—24no—
245C23×C4—24no—
246C23×C4—44no—
247C23×C4—44no—
248C23×C4—42no—
249C23×C4—42no—
250C23×C4C2×D414yes—
251C23×C4C2×Q814yes—
252C23×C4#4118yes—
253C23×C4#4114yes—
254C23×C4C2412yes—
255C23×C4C2412yes—
256C23×C4C2412yes—
257C23×C4C2412yes—
258C23×C4C2412yes—
259C23×C4C2412yes—
260C23×C4C2411yescharacteristic
261C23×C4C2411yescharacteristic
262C23×C4C2411yescharacteristic
263C23×C4C2411yescharacteristic
264C23×C4C2412yes—
265C23×C4C2412yes—
266C23×C4C2412yes—
267C23×C4C2412yes—
268C23×C4C2411yescharacteristic
269C23×C4C2412yes—
270C23×C4C2412yes—
271C23×C4C2411yescharacteristic
272#125—416no—
273C22⋊Q8—232no—
274C4×Q8—416no—
275C2×C4⋊C4—22no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—28no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—28no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—28no—
287C2×C4⋊C4—24no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—28no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—28no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—24no—
303C2×C4⋊C4—24no—
304C2×C4⋊C4—24no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—28no—
307C2×C4⋊C4—28no—
308C2×C4⋊C4—28no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—28no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—24no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—24no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—416no—
324C2×C4⋊C4—416no—
325C2×C4⋊C4—464no—
326C2×C4⋊C4—44no—
327C2×C4⋊C4—44no—
328C2×C4⋊C4—42no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—44no—
334C2×C4⋊C4—44no—
335C2×C4⋊C4—44no—
336C2×C4⋊C4C2×D414yes—
337C2×C4⋊C4C2×D414yes—
338C2×C4⋊C4C2×D4116yes—
339C2×C4⋊C4C2×Q814yes—
340C2×C4⋊C4C2×Q818yes—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—24no—
348C2×C22⋊C4—28no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4C2×D414yes—
351C2×C22⋊C4C2×D414yes—
352C2×C22⋊C4C2×Q818yes—
353C2×C42—232no—
354C2×C42—22no—
355C2×C42—24no—
356C2×C42—22no—
357C2×C42—22no—
358C2×C42—24no—
359C2×C42—24no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—24no—
374C2×C42—42no—
375C2×C42—44no—
376C2×C42C2×D414yes—
377C2×C42C2×D414yes—
378C2×C42C2×D414yes—
379C2×C42#4114yes—
380#95—24no—
381#95—24no—
382#95—24no—
383#95—24no—
384#95—24no—
385#95—24no—
386#95—24no—
387#95—24no—
388#95—28no—
389#95—24no—
390#95—24no—
391#95—28no—
392#95—28no—
393#95—24no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—28no—
398#95—24no—
399#95—28no—
400#95—24no—
401#95—28no—
402#95—44no—
403#95—44no—
404#95—44no—
405#95—44no—
406#95—44no—
407#95—44no—
408#95C2×D414yes—
409#95C2×D414yes—
410C24—21no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—21no—
415C24—22no—
416C24C22×D412yes—
417C24C22×Q812yes—
418C24C2×#4112yes—
419C24C2×#4114yes—
420C242−1+414yes—
421C24C2511yescharacteristic
422C2×Q8—28no—
423C2×Q8—28no—
424C2×Q8—28no—
425C2×Q8—44no—
426C2×Q8—44no—
427C2×Q8—44no—
428C2×Q8—44no—
429C22×C4—216no—
430C22×C4—216no—
431C22×C4—216no—
432C22×C4—216no—
433C22×C4—216no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—28no—
447C22×C4—28no—
448C22×C4—28no—
449C22×C4—216no—
450C22×C4—28no—
451C22×C4—28no—
452C22×C4—216no—
453C22×C4—28no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—24no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—24no—
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—24no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—416no—
525C22×C4—416no—
526C22×C4—48no—
527C22×C4—48no—
528C22×C4—84no—
529C22×C4—84no—
530C22×C4—88no—
531C22×C4—88no—
532C22×C4C22⋊Q8116yes—
533C22×C4C22×D412yes—
534C22×C4C22×D412yes—
535C22×C4C22×D412yes—
536C22×C4C22×D414yes—
537C22×C4C22×D414yes—
538C22×C4C22×D412yes—
539C22×C4C22×D412yes—
540C22×C4C22×D414yes—
541C22×C4C22×D412yes—
542C22×C4C22×D412yes—
543C22×C4C22×Q814yes—
544C22×C4C22×Q814yes—
545C22×C4C22×Q812yes—
546C22×C4C22×Q812yes—
547C22×C4C2×#4112yes—
548C22×C4C2×#4114yes—
549C22×C4C2×#4114yes—
550C22×C4C2×#4114yes—
551C22×C4C2×#4112yes—
552C22×C4C2×#4112yes—
553C22×C4H(5,𝔽2)14yes—
554C22×C4H(5,𝔽2)12yes—
555C22×C42−1+414yes—
556C22×C42−1+412yes—
557C4⋊C4—28no—
558C4⋊C4—216no—
559C4⋊C4—28no—
560C4⋊C4—28no—
561C4⋊C4—232no—
562C4⋊C4—48no—
563C4⋊C4—48no—
564C4⋊C4—416no—
565C4⋊C4—416no—
566C4⋊C4—48no—
567C4⋊C4—48no—
568C4⋊C4—48no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—48no—
573C4⋊C4—416no—
574C4⋊C4—44no—
575C4⋊C4—48no—
576C4⋊C4—84no—
577C4⋊C4—84no—
578C4⋊C4—84no—
579C22⋊C4—216no—
580C22⋊C4—28no—
581C22⋊C4—28no—
582C22⋊C4—48no—
583C22⋊C4—48no—
584C42—216no—
585C42—28no—
586C42—28no—
587C42—28no—
588C42—28no—
589C42—48no—
590C42—44no—
591C42—44no—
592C42—84no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—24no—
597C23—22no—
598C23—22no—
599C23—24no—
600C23—22no—
601C23—24no—
602C23—24no—
603C23—24no—
604C23—22no—
605C23—22no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23C2×C22⋊Q814yes—
612C23#53214yes—
613C23#53614yes—
614C23#55218yes—
615C23#55718yes—
616C23C23×D411yescharacteristic
617C23C23×D411yescharacteristic
618C23C23×Q811yescharacteristic
619C23C22×#4111yescharacteristic
620C23C22×#4111yescharacteristic
621C23C22×#4112yes—
622C23C2×H(5,𝔽2)11yescharacteristic
623C23C2×H(5,𝔽2)12yes—
624C23C2×2−1+412yes—
625C23C2×2−1+411yescharacteristic
626C23C2×2−1+412yes—
627Q8—416no—
628C2×C4—264no—
629C2×C4—24no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—24no—
638C2×C4—24no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—24no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—24no—
646C2×C4—24no—
647C2×C4—232no—
648C2×C4—24no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—24no—
658C2×C4—28no—
659C2×C4—28no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—28no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—44no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—44no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—42no—
720C2×C4—44no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—816no—
725C2×C4—816no—
726C2×C4C2×C22⋊Q814yes—
727C2×C4C2×C22⋊Q814yes—
728C2×C4#52514yes—
729C2×C4#53914yes—
730C2×C4D4214yes—
731C2×C4#54618yes—
732C2×C4#54714yes—
733C2×C4D4×Q814yes—
734C2×C4#55218yes—
735C2×C4#55414yes—
736C22—28no—
737C22—24no—
738C22—24no—
739C22—28no—
740C22—28no—
741C22—24no—
742C22—24no—
743C22—28no—
744C22—24no—
745C22—24no—
746C22#256518yescomplemented
747C22C22×C22⋊Q811yescharacteristic
748C22C2×#52511yescharacteristic
749C22C2×#53211yescharacteristic
750C22C2×#53611yescharacteristic
751C22C2×#53911yescharacteristic
752C22C2×D4211yescharacteristic
753C22C2×#54612yes—
754C22C2×#54711yescharacteristic
755C22C2×D4×Q811yescharacteristic
756C22C2×#55212yes—
757C22C2×#55212yes—
758C22C2×#55411yescharacteristic
759C22C2×#55712yes—
760C22#348612yes—
761C22#349212yes—
762C22#349212yes—
763C22#349811yescharacteristic
764C22#349911yescharacteristic
765C22#350312yes—
766C22#350812yes—
767C22#350912yes—
768C22#355212yes—
769C22#355212yes—
770C4—28no—
771C4—28no—
772C4—24no—
773C4—42no—
774C4—44no—
775C4—44no—
776C4—42no—
777C4—42no—
778C4—44no—
779C4—44no—
780C4—42no—
781C4—82no—
782C4—82no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4#244918yes—
788C2—28no—
789C2C2×#244911yescharacteristic
790C2C2×#256511yescharacteristic
791C2#3553211yescharacteristic
792C2#3612111yescharacteristic
793C2#3616312yes—
794C2#3618111yescharacteristic
795C2#3767511yescharacteristic
796C2#3786211yescharacteristic
797C2#3947612yes—
798C2#5914412yes—
799C2#5932112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#2565C2semidirect
5. #15629C2semidirect
6. #15434C2semidirect
7. #15240C2semidirect
8. #15228C2semidirect
9. #15184C2semidirect
10. #15151C2semidirect
14. #14049C2semidirect
15. #13976C2semidirect
16. #13909C2semidirect
746. C22#2565semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#25652
C2×#24422
C2×#23602
C22×#3842
#156292
#154342
#152402
#152282
#151842
#151512
#147862
#147022
#141392
#140492
#139762
#139092
#138822
#138812
C4×#3852